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On The Use Of Slope Limiters For The Design Of Recovery Based Error Indicators

M. Möller, D. Kuzmin
Published 2006 · Mathematics

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Gradient recovery techniques for the design of a posteriori error indicators are reviewed in the context of fluid dynamic problems featuring shocks and discontinuities. An edgewise slope limiting approach 24 tailored to linear finite element discretizations is presented. The improved gradient values at edge midpoints are recovered as the limited average of constant slopes from adjacent triangles. Furthermore, the low-order gradients may serve as natural upper and lower bounds to be imposed on the edge slopes. To this end, approved techniques such as averaging projection 33 , the (superconvergent) Zienkiewicz-Zhu patch recovery (SPR 34 ) and polynomial preserving recovery (PPR 29 ) are used to predict high-order gradients. A slope limiter is applied edge-by-edge to correct the provisional edge gradient values subject to geometric constraints. In either case, a second order accurate quadrature rule is employed to measure the difference between consistent and reconstructed slopes in the (local) L2-norm which provides a usable indicator for grid adaptation. The algebraic flux correction (AFC) methodology 14-19 is equipped with adaptive mesh refinement/coarsening procedures governed by the recovery based error indicator. The adaptive algorithm is applied to inviscid compressible flows at high Mach numbers.
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